### What is plasma?

Plasma is an ionized gas and is often referred to as the 4th state of matter. The characteristics vary depending on the plasma parameters such as gas pressure, plasma density, and electron temperature. Figure 1 shows the variety of plasmas observed in the universe. Debye length, λD, is the length scale associated with Coulomb shielding of the plasma and the Debye number is a parameter given by the average number of electrons in a Debye sphere, ND = (4/3) π λD3 n, where n is the number density. For ND much larger than 1, collective electrostatic interactions from all other particles in the Debye sphere dominate over binary collisions (weakly coupled plasma) whereas ND smaller than 1 is strongly coupled plasma.

 Figure 1: Variety of plasmas, characterized by electron density and temperature. Lines indicate constant Debye length and Debye number.

### Plasma propulsion for in-space missions

Thrust and specific impulse are two important key performance parameters for space propulsion systems, as shown in Figure 2. There are various acceleration mechanisms of propellant, including chemical, nuclear, beam, and electric propulsion. In particular, electric propulsion (EP) is used in modern spacecraft for station keeping and orbit raising due to its high specific impulse. Three main EP technologies include electrostatic (ions are accelerated by electric field), electromagnetic (ions are accelerated by both electric and magnetic fields), and electrothermal (gas is heated by electricity) mechanisms. Based on the Tsiolkovsky's rocket equation, the higher the specific impulse, the less propellant mass required for a given ΔV mission. Additionally, thrust is an important measure that determines the mission time.

 Figure 2: In-space propulsion systems.

### Why modeling and simulation?

In order to obtain a "truth" (i.e. what the universe does), one can use measurements (experiments) or theoretical modeling, in which one approximates a physical system using mathematical description. While some theoretical frameworks can directly derive an analytic (exact) solution, the majority must rely on computer simulations to obtain such solutions. This is often the case to solve real-life problems as the problems get more and more nonlinear and complex. Hence, computer simulation is often the only tool to obtain a mathematical "solution". In PDML, we use theoretical models and computer simulation in order to understand complex plasma physics phenomena. As can be seen from Figure 3, strong collaborations between experimentalists, theorists, and computational modelers are essential to advancing our understanding of a physical problem.

 Figure 3: Relation between measurements, theory, and computer simulations (Acknowledgement: Professor Bram Van Leer)